Problem 1672. Leftovers? Again?!

I am thinking of a positive number X. To determine what number I am thinking of, I will give you two 1xN vectors. The first vector (V1) is several numbers, none of which will share a factor. The second vector (V2) is the remainder of X when divided by each of the numbers in V1. Calculate what the lowest possible value of X can be given these criteria. For example:

V1 = [2 3] ; V2 = [1 2]

would give an X value of 5. There are an infinite number of other values of X that would satisfy V1 and V2, but I want the lowest one.